At the end of the first section after the lava pit, do not go into the tube at the end. It will bring you to an icy secret area that has no coins and just one [?] block. Also, skip the [?] block before the lava jumps as it will give you a mushroom no matter what your Mario is equipped as.

To get to the secret exit, get a blue Yoshi in the beginning. Other Yoshis won't work, because a vine has to be climbed.(or hit the Qbox right after the vine, there will be a Yoshi) Keep him until you see the key near the end. Use him to grab and hold the key in his mouth, then walk into the keyhole. This leads to Star Road, and the real exit is not too far, just two jumps and you're done.